Convection-dominated accretion flows

Nonradiating advection-dominated accretion flows are convectively unstable in the radial direction. We calculate the two-dimensional (r-theta) structure of such flows assuming that (1) convection transports angular momentum inward, opposite to normal viscosity, and (2) viscous transport by other mechanisms (e.g., magnetic fields) is weak (alpha much less than 1). Under such conditions convection dominates the dynamics of the accretion flow and leads to a steady state structure that is marginally stable to convection. We show that the marginally stable flow has a constant temperature and rotational velocity on spherical shells, a net flux of energy from small to large radii, zero net accretion rate, and a radial density profile of rho proportional to r(-1/2) flatter than the rho proportional to r(-3/2) profile characteristic of spherical accretion flows. This solution accurately describes the full two-dimensional structure of recent axisymmetric numerical simulations of advection-dominated accretion flows.